Direct Variation/ Constant of Proportionality

Front

What is direct variation?

Back

Direct variation is a relationship between two variables where one variable is a constant multiple of the other. It can be expressed as y = kx, where k is the constant of proportionality.

Front

What is the constant of proportionality?

Back

The constant of proportionality (k) is the constant factor that relates two variables in a direct variation. It represents the ratio of y to x.

Front

Which graph represents a direct variation?

Back

A graph of direct variation is a straight line that passes through the origin (0,0).

Front

Write the equation for a direct variation where k = 3.

Back

y = 3x.

Front

If y = 4 when x = 2, what is the constant of proportionality (k)?

Back

k = 2, because y = kx implies 4 = k(2), so k = 4/2.

Front

What is the independent variable in a direct variation?

Back

The independent variable is the variable that is changed or controlled in an experiment, typically represented by x.

Front

What is the dependent variable in a direct variation?

Back

The dependent variable is the variable that is measured or affected in an experiment, typically represented by y.

Front

If the cost of 5 reams of paper is $12.75, what is the cost per ream?

Back

The cost per ream is $2.55, calculated by dividing the total cost by the number of reams: $12.75 / 5.

Front

Is the relationship y = 2x + 3 a direct variation?

Back

No, because it does not pass through the origin; it has a y-intercept of 3.

Front

How can you tell if a table of values represents a direct variation?

Back

If the ratio of y to x is constant for all pairs of values, it represents a direct variation.